Finite Population Correction Factor Or Fpcf)
If a specified population is relatively of small size and sample size is more than 5 percent of the population then the standard error must be adjusted by multiplying it by the finite population correction factor as:
FPCF is described by =
Whereas N = population size
n = sample size
Illustration
A manager wants an estimate of sales of salesmen in his company. A random sample 100 out of 500 salesmen is chosen and average sales are found to be Shs. 75,000. If a sample standard deviation is Shs. 15000 then determines the population mean at 99 percent level of confidence
Solution
Now N = 500, n = 100, x¯ = 75000 and S = 15000
Here
Standard error of mean
S_{x¯ = }(s/√n) * {}
= (15,000/√100) * (√ {(500 - 100)/(500 - 1)})
= (15,000/10) * (0.895)
S_{x¯ }= 1342.50 at 99 percent level of confidence
Population mean = x¯ ± 2.58 S_{x¯}
=shs 75000 ± 2.58(1342.50)
=shs 75000 ± 3464
= Shs 71536 to 78464